This paper introduces an integrated physics–machine learning framework to model unsteady magnetohydrodynamic free convection in a micropolar fluid over a porous vertical sheet subjected to suction and Lorentz forces. Unlike traditional studies that rely solely on numerical solvers, this approach couples finite difference-based numerical simulations with a trained artificial neural network (ANN) model, offering a predictive, data-driven perspective on a highly nonlinear transport problem. The governing equations, transformed through similarity analysis, account for microrotation, thermal diffusion (Dufour effect), and mass diffusion (Soret effect). Results demonstrate that the ANN can accurately anticipate key flow features such as velocity suppression under magnetic damping and thermal enhancement via micro rotational coupling without re-solving the partial differential equations (PDEs). This hybrid paradigm validates the ANN against benchmark numerical results and showcases its potential to rapidly explore parameter spaces in real-time applications. Such a predictive tool holds promise for the design of next-generation heat management systems, magnetically controlled microfluidic devices, and smart porous media applications. This hybrid paradigm validates the ANN against benchmark numerical results and showcases its potential to rapidly explore parameter spaces in real-time applications. The model successfully addresses three key research questions: (i) accurate prediction of flow and transport dynamics without solving PDEs, (ii) utilization of artificial intelligence for sensitivity analysis and optimization, and (iii) quantitative assessment of the impact of key physical parameters on the system's thermal and hydrodynamic performance.
Mahboobtosi et al. (Fri,) studied this question.